Gamma Dose Rate Point Source Calculator

Q: What is the dose rate at one metre from a 370 GBq iridium-192 source?

Between 40 and 48 mGy/h, and the width of that answer is the honest part. Iridium-192's air kerma rate constant is published as 108 to 130 µGy·m²/(GBq·h) — a 20 per cent span — so 370 GBq at one metre is 39,960 µGy/h at the bottom of the range and 48,100 at the top. The long-established old-unit factor of 4.8 R·cm²/(mCi·h) gives 4.8 R/h for 10 Ci at a metre, which is 42,048 µGy/h and sits between them. Summing the nine gamma lines from first principles gives 106.1 for the constant, 93 per cent of the old-unit figure, the shortfall being the weak lines and X-rays a gamma-only sum leaves out. Whichever you use, the practical reading is the same: an unshielded minute at a metre is of the order of 700 µGy.

Q: How do I convert an old R·cm²/(mCi·h) gamma constant?

Multiply by 23.68 to get µGy·m²/(GBq·h). The factor is three conversions in one: one roentgen is 8.76 mGy of air kerma (from the roentgen's definition of 2.58×10−4 C/kg and a mean energy per ion pair in air of 33.97 J/C), one millicurie is 0.037 GBq, and a square centimetre is 10−4 of a square metre. So caesium-137's 3.3 becomes 78.1, cobalt-60's 13.2 becomes 312.5, iridium-192's 4.8 becomes 113.6 and radium-226's 8.25 becomes 195.3. Note that this conversion changes the units and not the quantity: both numbers are AIR KERMA. A constant published in mSv·m²/(GBq·h) of ambient dose equivalent is a different quantity, roughly 20 per cent larger at caesium energies, and is not interchangeable with either.

The dose rate from a point gamma source, with the air kerma rate constant printed as the published range it really is, the first-principles derivation beside it, optional narrow-beam shielding, and the inverse solved — the distance at which the rate falls to a figure you name.

Last updated 7 Oct 2026

A dose or dose rate calculated here is an estimate from a published model, not a measurement of anybody. Where a page prints a published limit beside its answer, that limit is there for comparison only — it is not permission and it is not a finding that an exposure is acceptable. Occupational and patient dose are governed by regulation and by local policy, and a dosimeter, a survey meter or a medical physicist's own calculation takes precedence over anything on this site.

Gamma dose rate from a point source

Nuclide, activity and distance → rate, time and distance

NuclideFourteen nuclides, twelve of them with a published air kerma rate constant and two without. Yttrium-90 and strontium-90 are on the list on purpose: they are PURE BETA emitters, this page refuses them rather than returning a near-zero gamma rate, and the reason is that their external hazard is real and is not gamma — it is bremsstrahlung made in whatever the betas stop in, plus a skin dose at contact. The last option takes a constant you type, for any nuclide at all.

Which end of the published range to compute withThe air kerma rate constant is not a single agreed number. Compilations differ by 10 to 20 per cent for the clean gamma emitters, and by a factor of two or three for the nuclides whose characteristic X-rays carry the dose, depending on which lines they include and where they put the low-energy cut-off. So this page carries a RANGE for every nuclide and lets you choose which end to work from. The default is the upper end because that is the protective choice; the rate at all three is printed below, so you can see how much the choice is worth. For iridium-192 the range is 108 to 130 and the span is 20 per cent, which is larger than most of the other uncertainties on this page put together.

…or the constant itselfIn µGy·m²/(GBq·h) — the air kerma rate at one metre from one gigabecquerel for one hour. Locked while a nuclide and a range end are selected. If your source is specified in the old units, multiply R·cm²/(mCi·h) by 23.68: caesium-137’s 3.3 becomes 78.1 and cobalt-60’s 13.2 becomes 312.5.

ActivityThe activity NOW, not at calibration. A sealed source decays on the shelf and an iridium-192 source loses a quarter of its activity every month, so a certificate six months old is wrong by a factor of five and a half.

…inOne curie is 3.7×10¹⁰ becquerel by definition rather than by measurement, so the curie options are a rename of the becquerel ones and carry no uncertainty of their own. Sealed sources are still specified in curies almost everywhere outside Europe: a 10 Ci iridium-192 radiography source is 370 GBq, and a 20 mCi technetium generator elution is 740 MBq.

Distance from the sourceCentre of the source to the point of interest. The model is a POINT source, which is a good approximation beyond about three times the source’s own longest dimension and a poor one inside that — at the surface of a real capsule the inverse square law over-states the rate badly, and at contact there is no sensible distance to put in at all.

…inMetres by default, because the air kerma rate constant is defined at one metre. Feet are here for American industrial radiography, where the old rule of thumb and the published R·cm²/(mCi·h) constants are both quoted at one foot.

Shielding materialOnly used when the thickness below is above zero. Eight materials, every coefficient from NIST’s X-Ray Mass Attenuation Coefficients tables — a work of the United States Government, which is why they can be printed here rather than cited from a copyrighted standard. Lead first because it is the default, and the reason it is the default is its atomic number rather than its density.

Shielding thicknessIn millimetres, because that is the unit lead is specified and ordered in; 300 mm is the top of the field, which is well past where a closed-form answer means anything. Zero gives the unshielded rate exactly, which is the sanity check: the shielded and unshielded rows are then identical to the last digit.

Photon energy for the attenuationIn MeV, and locked while a listed nuclide is selected. The figure it fills in is the AIR-KERMA-WEIGHTED mean of that nuclide’s gamma lines — each line weighted by its own contribution to the constant rather than by its emission probability, because it is the dose that is being attenuated. For iridium-192 that is 399 keV, which is above both its yield-weighted mean of 372 keV and the conventional 380 the shielding pages on this site use, and within 0.4 per cent of the energy-fluence-weighted 398 those pages also quote.

DensityNIST’s coefficient is per GRAM, so a density has to come from somewhere else before it becomes a per-centimetre attenuation, and that density is a property of your material rather than of the coefficient. Ordinary structural concrete runs 2.2 to 2.4 g/cm3 and much more loaded with barytes; rolled lead sheet is close to theoretical and leaded acrylic is nowhere near it.

DensityIn g/cm3, locked while the conventional value is in use. The values used are NIST’s own table entries: lead 11.35, tungsten 19.30, iron 7.874, aluminium 2.699, concrete 2.300, water 1.000, ICRU-44 soft tissue 1.060 and dry air 0.0012048.

A dose you want the time forIn µGy of air kerma. The page prints how long it takes to accumulate that at the rate above. 1000 µGy is one milligray, which is a convenient unit to think in because it is roughly a third of a year’s natural background — and at the default it takes under eighteen minutes.

…and a rate you want the distance forIn µGy/h. The page solves the inverse: how far away the rate falls to this. It is the question that matters when nobody can shield — a barrier at a distance is often the only control available on a site. 7.5 µGy/h is here as a round number that happens to be near several published boundary design figures; it is a NUMBER YOU NAME and this page attaches no regulatory meaning to it.

Not a circuit: the inverse square law drawn on logarithmic axes, where it is a straight line of gradient minus two, with both axes measured relative to where you are standing. The cross at the centre is you. The second cross is where you would have to stand for the rate to fall to the target you named – and because the gradient is exactly minus two, the distance you need and the reduction you asked for are the same point on the line, read off two different axes. Below the plot the shield's transmission is hatched to scale across the same width, so the two controls a radiation worker has are set side by side.

3.407mGy/hExample

A 370 GBq iridium-192 radiography source — 10 curies, the ordinary size — at one metre, behind 10 mm of lead, at the upper end of the published constant

One inverse square law, one exponential, and the constant that is a range

ᶠ = Γ·A/d² · e^−μx · d(target) = √(Γ·A·T/ᶠₜ) · Γ = (1/4π)·Σ yᵢEᵢ·(μₑₙ/ρ)ₐᵢד(Eᵢ)

Γ: the air kerma rate constant, µGy·m²/(GBq·h): the air kerma rate at one metre from one gigabecquerel. It is a property of the nuclide’s decay scheme and of nothing else — not of the source’s size, not of its encapsulation. It is tabulated as a RANGE here because compilations disagree — by 10 to 20 per cent for the clean gamma emitters and by a factor of two or three where characteristic X-rays carry the dose — and the page prints both ends
A, d: activity now, and distance from the centre of the source. Both enter the simplest way they can: the rate is LINEAR in activity and goes as the INVERSE SQUARE of distance, so doubling the activity doubles the rate and doubling the distance quarters it. The inverse square is geometry rather than physics — the same photons spread over four times the area — and it fails only where the source stops looking like a point
e^(−μx): narrow-beam attenuation through a shield, with μ from the NIST coefficient at the photon energy and the density. Zero thickness gives exactly 1, which is the check. It is a NARROW-BEAM term and therefore optimistic: a real shield scatters photons back into the beam and published half-value layers are 11 to 33 per cent larger than ln2/μ for that reason
(μ_en/ρ)_air: the mass energy-ABSORPTION coefficient of air, cm²/g, which is a different NIST column from the μ/ρ that attenuates. One is what leaves the beam; the other is what gets deposited. Confusing them is the commonest error in this derivation after the 4π
1/4π: the isotropic point-source fluence factor, and the term everybody drops. Photons from a point source spread over the surface of a sphere, so the fluence at distance d is A/(4πd²). Leave the 4π out and the answer is 12.57 times too big. The open-access chapter this plugin’s data module consulted for the tabulated constants prints the factor as π/4, which is sixteen times smaller again and is simply wrong, and that is why the constants here are the conventionally published ones rather than that chapter’s
Σ yᵢEᵢ: the total gamma energy emitted per decay, in MeV, and the whole input to the old rule of thumb: 6 R/h per curie at one foot per MeV emitted, which in SI is 132 µGy·m²/(GBq·h) per MeV. It is one multiplication and it lands within 9 per cent of the line sum for every nuclide in the table above whose mean photon energy is above 300 keV, which makes it a genuinely useful check there and a hopeless one for iodine-125
d(target): the inverse, and the practical question when nobody can shield. It is the exact inverse of the forward calculation: the square root of Γ·A·T divided by the rate you want. Note the square root — the single commonest slip here is to divide rather than to take the root, which gives the right answer only when the right answer happens to be one metre

Worked example

A 370 GBq iridium-192 radiography source — 10 curies, the ordinary size — at one metre, behind 10 mm of lead, at the upper end of the published constant
THE CONSTANT, AND WHY IT IS A RANGE. Iridium-192's air kerma rate constant is published as 108 to 130 µGy·m²/(GBq·h) — a span of 1.204 — and this example takes the upper end, which is the protective choice. The first-principles sum of its nine gamma lines gives 106.07, which is 0.891 times the midpoint of the range. The old R·cm²/(mCi·h) factor of 4.8, converted independently, gives 113.6. Three routes, all inside the published range, none of them identical
THE RATE, BEFORE ANY SHIELD. 130 × 370 GBq ÷ 1² = 48,100 µGy/h, which is 48.10 mGy/h. For comparison the old units give 4.8 R/h at one metre for 10 Ci, and 4.8 R is 42,048 µGy — inside the range, nearer the bottom of it. This is a serious rate: an unshielded minute at a metre is 802 µGy
THE SHIELD, AND THE ENERGY IT IS COMPUTED AT. Nine lines from 206 to 612 keV cannot be attenuated with one coefficient honestly, so the page uses the AIR-KERMA-WEIGHTED mean of them, 399.2 keV — each line weighted by its own contribution to the constant, because it is the dose that is being attenuated. Lead's μ/ρ there is 0.233245 cm²/g, read in LOG-LOG space from the NIST grid, so μ = 0.233245 × 11.35 = 2.6473 per cm and the narrow-beam half-value layer is 2.618 mm
WHAT 10 MM OF LEAD DOES. 10 mm is 3.819 half-value layers, so the transmission is 2 to the minus that: 7.084 per cent, or one part in 14.1. The rate behind it is 48,100 × 0.070840 = 3,407.4 µGy/h. Note that this is a narrow-beam number and is therefore the optimistic one; a real collimator and a real room scatter photons round the geometry this calculation can see
DISTANCE AND SHIELDING IN THE SAME CURRENCY. That 10 mm of lead is worth 3.819 half-value layers, and a half-value layer is half a doubling of distance, so the shield is worth 1.91 doublings — the same protection as standing 3.76 times further away. At one metre that means 10 mm of lead buys you as much as retreating to 3.76 m, which on an open site is usually the cheaper of the two
THE TIME, WHICH IS THE PART PEOPLE GET WRONG. One milligray of air kerma, 1000 µGy, takes 17.6 minutes behind the shield. With the shield removed it takes 74.8 seconds. That is the whole argument for shielding a source you have to work near, and it is also the argument for never assuming a source is shielded because it usually is
AND THE INVERSE, WHICH IS WHAT YOU ASK WHEN YOU CANNOT SHIELD. The rate falls to 7.5 µGy/h at 21.31 m behind the 10 mm of lead, and at 80.1 m with no shield at all. Those two numbers are the barrier distance with and without the collimator, and the difference between them — a factor of 3.76 — is the same factor the shield bought in the step above, because distance and attenuation multiply independently. Both figures are DISTANCES THIS PAGE COMPUTED, not boundaries anybody has approved

The air kerma rate constant three ways: published range, first-principles sum, and one multiplication

All constants in µGy·m²/(GBq·h). The first two columns are the published range, which is a range because compilations disagree over which lines and what low-energy cut-off they include: by 10 to 20 per cent for the clean gamma emitters and by a factor of 2.2 for americium-241 and 3.2 for iodine-125, where the X-rays carry the dose. The third is (1/4π)·Σ y·E·(μ_en/ρ)_air computed from the NPL line list and the NIST air table, and the fourth is the ratio between them, which is the column worth reading. For the eight nuclides here whose mean photon energy is above 300 keV it sits at 0.82 to 0.94 — the derivation is a few per cent LOW, always in the same direction, because a gamma-only sum omits the weak lines and the characteristic X-rays. For iodine-125 it is 0.20, a factor of five, because the 35.5 keV gamma comes out in only 6.7 per cent of decays while the tellurium K X-rays come out at around 140 per cent: for that nuclide the X-rays ARE the dose and a gamma-only sum is not an approximation to it. And for COBALT-57 the ratio is 1.49, which breaks the pattern in the other direction and is the most instructive cell in the table — its 14.41 keV line carries 41 per cent of the uncut sum, because air absorbs 63 times as strongly at 14 keV as at 122 keV, and a published constant with a 20 keV cut-off excludes it. Drop that one line and the sum is 13.19, which is the bottom of the published range. The last two columns are the old 6·C·E·n rule of thumb in SI clothing: one multiplication, 132 times the total gamma energy emitted per decay, and it lands within 9 per cent of the line sum for every nuclide here whose mean photon energy is above 300 keV — the worst of those eight is 8.1 per cent out. Below that it fails, because the air coefficient it implicitly assumes is a high-energy one: it is 29 per cent low for cobalt-57, 21 per cent low for americium-241 and 17 per cent high for technetium-99m. This sums the PRINCIPAL GAMMA lines only. It omits the many weak lines and, more importantly, the characteristic X-rays that follow electron capture and internal conversion. For a clean gamma emitter that makes the sum a few per cent low; for an electron-capture nuclide it can be most of the answer — iodine-125 emits its 35.5 keV gamma in only 6.7 per cent of decays while its tellurium K X-rays come out at around 140 per cent, so a gamma-only sum understates its air kerma rate by a factor of several.
Nuclide	Published, low	Published, high	Derived from the lines	Derived ÷ midpoint	Lines summed	Σ yᵢEᵢ (MeV)	132 × Σ yᵢEᵢ
Tc-99m	19.0	23.0	14.173	0.675×	1	0.1251	16.51
F-18	130.0	156.0	134.511	0.941×	1	0.9886	130.47
I-131	50.0	66.0	50.235	0.866×	5	0.3750	49.49
I-125	2.5	8.0	1.041	0.198×	1	0.0024	0.31
Y-90	—	—	—	—	—	—	PURE BETA — no gamma to sum, and this page refuses it
Ir-192	108.0	130.0	106.065	0.891×	9	0.7933	104.70
Co-57	13.0	17.0	22.347	1.490×	3	0.1204	15.89
Mn-54	110.0	130.0	109.718	0.914×	1	0.8346	110.15
Na-22	290.0	330.0	280.124	0.904×	2	2.1926	289.36
Co-60	300.0	351.0	305.633	0.939×	2	2.5037	330.42
Cs-137	77.0	93.0	75.689	0.890×	1	0.5631	74.31
Ba-133	50.0	65.0	47.151	0.820×	5	0.3581	47.27
Sr-90	—	—	—	—	—	—	PURE BETA — no gamma to sum, and this page refuses it
Am-241	2.5	5.5	3.642	0.910×	2	0.0219	2.89

Dose rate per gigabecquerel, at the distances people actually stand

Per gigabecquerel, at the upper end of each published range, unshielded. Multiply by your own activity in GBq and the whole table scales, because the rate is linear in activity and nothing else in it is. The 10 cm column is in MILLIGRAY per hour and the rest are in micrograys, which is the first thing worth noticing: moving from 10 cm to 1 m divides the rate by a hundred, and moving from 10 cm to 10 m divides it by ten thousand. The second is the span down the columns. One gigabecquerel is a routine nuclear medicine quantity and a trivial industrial one, and at one metre it gives 23 µGy/h of technetium-99m against 351 of cobalt-60 — a factor of fifteen for the same number of decays, entirely because of what energy those decays come out at. The third is what the table says about handling: at 10 cm, which is about where a hand is when it holds a vial, a gigabecquerel of fluorine-18 is 15.6 mGy/h, so an unshielded minute is 260 µGy to the skin of the fingers. That is why PET syringes live in tungsten. This page computes physics. It is not a compliance determination, and where it prints a published limit beside an answer that limit is shown for comparison and never as permission. Radiation work is governed by regulation and by local policy, and a measurement takes precedence over anything calculated here.
Nuclide	Γ (upper end)	at 10 cm (mGy/h)	at 30 cm (µGy/h)	at 1 m (µGy/h)	at 2 m (µGy/h)	at 5 m (µGy/h)	at 10 m (µGy/h)
Tc-99m	23.0	2.30	255.6	23.0	5.75	0.920	0.2300
F-18	156.0	15.60	1,733.3	156.0	39.00	6.240	1.5600
I-131	66.0	6.60	733.3	66.0	16.50	2.640	0.6600
Ir-192	130.0	13.00	1,444.4	130.0	32.50	5.200	1.3000
Cs-137	93.0	9.30	1,033.3	93.0	23.25	3.720	0.9300
Co-60	351.0	35.10	3,900.0	351.0	87.75	14.040	3.5100

Distance against shielding, in the same currency

The two controls a radiation worker has are distance and shielding, and this table puts them in one unit so they can be traded against each other. A factor of four in rate is EXACTLY two half-value layers, for every material at every energy, because that is arithmetic rather than physics: n half-value layers is 2⁻ⁿ, so the equivalent of multiplying the distance by f is 2·log₂(f) layers. Doubling the distance is worth two layers; ten times the distance is worth 6.64, which for iridium-192 is 17.4 mm of lead or 20.4 cm of concrete. The practical reading runs both ways. Distance is free, needs no structure to hold it up and protects everybody in the room, so it is always the first control — and it does not work when the job has to be done at arm’s length, which is where shielding and time are all that is left. Note the 31.62 row: the square root of a thousand, so a thousandfold reduction needs 31.6 times the distance or ten half-value layers, and whichever of those is available is usually not a choice. This is NARROW-BEAM attenuation: one uniform slab, a parallel beam, and every scattered photon assumed lost. A real shield scatters photons back into the beam, and the published half-value layers in shielding tables are 11 to 33 per cent LARGER than ln2/μ for exactly that reason. A narrow-beam answer therefore UNDER-states the shield a real room needs, which is the unsafe direction, and closing that gap is what a build-up factor is for. The coefficient is interpolated in log-log space between NIST’s tabulated energies. Measured by leave-one-out on that grid the interpolation is good to about 1 to 2 per cent through the Compton region, and up to 13 per cent in the steep photoelectric region below 40 keV in low-Z materials. The grid itself stops at 1 keV and 20 MeV, and outside it this page returns nothing rather than an extrapolation.
Multiply the distance by	Rate becomes	…or one part in	Equivalent half-value layers	mm of lead at Ir-192’s 399 keV	cm of concrete, same
1.00×	1	1 in 1.00	0.0000	0.000	0.00
1.50×	0.44444444	1 in 2.25	1.1699	3.063	3.60
2.00×	0.25	1 in 4.00	2.0000	5.237	6.16
2.50×	0.16	1 in 6.25	2.6439	6.922	8.14
3.00×	0.11111111	1 in 9.00	3.1699	8.300	9.76
4.00×	0.0625	1 in 16.00	4.0000	10.473	12.31
5.00×	0.04	1 in 25.00	4.6439	12.159	14.29
7.00×	0.02040816	1 in 49.00	5.6147	14.701	17.28
10.00×	0.01	1 in 100.00	6.6439	17.396	20.45
20.00×	0.0025	1 in 400.00	8.6439	22.632	26.61
31.62×	0.00100018	1 in 999.82	9.9655	26.093	30.67
100.00×	0.0001	1 in 10,000.00	13.2877	34.791	40.90

Where the constant comes from, line by line

Every line of six nuclides, with the air coefficient at that energy and the contribution it makes to µGy·m²/(GBq·h). Three things are visible here that a single constant hides. FIRST, the coefficient column is not flat: air’s mass energy-absorption coefficient is 0.0241 cm²/g at 122 keV and 1.511 at 14.4 keV, sixty-three times larger, because the photoelectric cross-section is climbing steeply as the energy falls. That is why cobalt-57’s smallest line is its biggest contributor and why a low-energy cut-off changes the answer so much. SECOND, iridium-192’s nine lines are not interchangeable: the 316 keV line is the largest single contributor but no one line is half the total, which is exactly the case a single-energy shielding calculation cannot represent. THIRD, americium-241’s 59.5 keV line does 83 per cent of its work and its 26.3 keV line the rest — and both are low enough that the capsule, the air path and the shielding behave quite differently from a caesium source. Note what is NOT in this table: the characteristic X-rays. They are the reason the sums are low. This sums the PRINCIPAL GAMMA lines only. It omits the many weak lines and, more importantly, the characteristic X-rays that follow electron capture and internal conversion. For a clean gamma emitter that makes the sum a few per cent low; for an electron-capture nuclide it can be most of the answer — iodine-125 emits its 35.5 keV gamma in only 6.7 per cent of decays while its tellurium K X-rays come out at around 140 per cent, so a gamma-only sum understates its air kerma rate by a factor of several.
Nuclide	Line energy (keV)	Emitted in (%)	μ_en/ρ of air (cm²/g)	Contribution	Share of the sum (%)
Co-60	1,173.23	99.85	0.02700	145.1971	47.5
Co-60	1,332.49	99.98	0.02624	160.4357	52.5
Cs-137	661.66	85.10	0.02929	75.6894	100.0
Ir-192	205.79	3.30	0.02686	0.8371	0.8
Ir-192	295.96	28.72	0.02865	11.1776	10.5
Ir-192	308.45	29.68	0.02879	12.0991	11.4
Ir-192	316.51	82.75	0.02886	34.6958	32.7
Ir-192	468.07	47.81	0.02961	30.4134	28.7
Ir-192	484.57	3.18	0.02964	2.0961	2.0
Ir-192	588.58	4.52	0.02954	3.6075	3.4
Ir-192	604.41	8.20	0.02951	6.7134	6.3
Ir-192	612.46	5.34	0.02948	4.4252	4.2
Co-57	14.41	9.16	1.51142	9.1588	41.0
Co-57	122.06	85.60	0.02408	11.5460	51.7
Co-57	136.47	10.68	0.02455	1.6424	7.3
Am-241	26.34	2.27	0.22976	0.6307	17.3
Am-241	59.54	35.78	0.03079	3.0112	82.7
I-125	35.49	6.68	0.09570	1.0415	100.0

One inverse square law, a constant that is a range, and the two nuclides this page will not answer for

Γ·A/d² is the whole of it, and the only hard part is Γ. The dose rate from a point gamma source is the air kerma rate constant times the activity divided by the square of the distance. Activity and distance you know or can measure. Γ is a property of the decay scheme that somebody else has computed, and the awkward fact about it is that the published values DISAGREE — by 10 to 20 per cent for the clean gamma emitters and by a factor of two or three where characteristic X-rays carry the dose, depending on which gamma lines a compilation includes and where it puts its low-energy cut-off. So this page carries a range for every nuclide, defaults to the upper end because that is the protective choice, and prints the rate at both ends so the size of the disagreement is visible rather than hidden in a citation.

The derivation is on the page because it is the one check you can do yourself. Γ is computable from the emission lines and the mass energy-absorption coefficient of air: (1/4π)·Σ y·E·(μ_en/ρ)_air, summed over the lines. Done from the NPL line list and the NIST air table it comes out 2 to 7 per cent BELOW the published constants for the clean gamma emitters — cobalt-60 at 0.978 of the independently converted old-unit factor, caesium-137 at 0.969, iridium-192 at 0.933, iodine-131 at 0.964 — and the residual is not noise. A gamma-only line sum omits the weak lines and, more importantly, the characteristic X-rays that follow electron capture and internal conversion. For an electron-capture nuclide that omission is most of the answer: iodine-125’s gamma-only sum is 1.04 against a published 2.5 to 8, because the 35.5 keV gamma is emitted in 6.7 per cent of decays while its tellurium K X-rays come out at around 140 per cent. The X-rays are the dose. If you sum the lines yourself and get a smaller number than the table, that is why.

The 1/4π is the term that gets dropped, and cobalt-57 is the exception that explains the cut-off. Photons from a point source spread over the surface of a sphere, so the fluence is A/(4πd²) and leaving the 4π out over-states the constant by 12.57 times. This plugin’s own data module records that the open-access chapter consulted for the tabulated constants prints the factor as π/4, which is a different number again, and that is why the constants here are the conventionally published ones. The other instructive case runs the opposite way. Cobalt-57 derives at 22.35 against a published 13 to 17 — too HIGH — because its 14.41 keV line, emitted in only 9.2 per cent of decays, sits where air’s absorption coefficient is 63 times what it is at 122 keV, and carries 41 per cent of the uncut sum. Published constants apply a low-energy cut-off, and the physical justification is blunt: a 14 keV photon does not leave the capsule. Cut at 20 keV and the sum is 13.19, the bottom of the published range.

Distance and shielding are the same currency, and distance is usually cheaper. A factor of four in dose rate is exactly two half-value layers, for every material at every energy, because that is arithmetic and not physics. So doubling the distance is worth two half-value layers of anything, and multiplying the distance by ten is worth 6.64 — which for iridium-192 is 17.4 mm of lead or 20.4 cm of concrete. Distance needs no structure to hold it up, costs nothing and protects everybody in the room, which is why it is the first control in practice and why barrier distance rather than barrier thickness is what gets argued about on an industrial radiography site. Shielding wins where the job has to be done at arm’s length. The page prints the shield you entered in millimetres, in half-value layers AND in doublings of distance, so the trade can be made in one glance.

Why the page refuses yttrium-90 and strontium-90. They are pure beta emitters and have no useful gamma emission at all, so a gamma dose-rate formula would return something close to zero for them — and a reader who saw that number might reasonably conclude there was no external hazard. There is. The betas make BREMSSTRAHLUNG in whatever they stop in, which is a real penetrating dose and is WORSE in a high-Z shield, so a yttrium-90 source wants perspex before lead rather than lead alone. And the betas themselves deliver a large skin dose at contact that no air-kerma-at-a-distance calculation can see: yttrium-90’s beta has a maximum energy of 2.28 MeV and a range of the order of a centimetre in tissue, which is metres in air for the same reason every other range scales — a range in grams per square centimetre divided by a density, and air is 880 times less dense than tissue. So the headline goes blank for those two, which is the only honest output this page can produce for them.

What this page cannot do, said plainly. It models a POINT source in empty space, so it has no source extent, no capsule, no self-absorption, no air attenuation, no floor and no walls, and all of those matter: inside about three times the source’s own length the inverse square law over-states the rate, and across a large hall air absorption under-states the protection. Its shielding term is NARROW-BEAM, with no build-up factor, which under-states the thickness a real room needs — the half-value layer page on this site prints the published broad-beam figure beside the calculated one and measures the gap. It computes AIR KERMA, which is not dose equivalent and not effective dose — the conversion from air kerma to ambient dose equivalent H*(10) is around 1.20 Sv/Gy at caesium-137 energies, a second-hand figure the shielding pages on this site carry and flag as such, and it is energy-dependent, so treating a microgray as a microsievert under-states the dose quantity by about a fifth there. And it renders no verdict: there is no distance, time or thickness on this page that is adequate, compliant or permitted, because those are dose constraints, occupancy factors and a regulator, and none of them is a decay scheme.

Frequently asked questions

What is the dose rate at one metre from a 370 GBq iridium-192 source?

Between 40 and 48 mGy/h, and the width of that answer is the honest part. Iridium-192’s air kerma rate constant is published as 108 to 130 µGy·m²/(GBq·h) — a 20 per cent span — so 370 GBq at one metre is 39,960 µGy/h at the bottom of the range and 48,100 at the top. The long-established old-unit factor of 4.8 R·cm²/(mCi·h) gives 4.8 R/h for 10 Ci at a metre, which is 42,048 µGy/h and sits between them. Summing the nine gamma lines from first principles gives 106.1 for the constant, 93 per cent of the old-unit figure, the shortfall being the weak lines and X-rays a gamma-only sum leaves out. Whichever you use, the practical reading is the same: an unshielded minute at a metre is of the order of 700 µGy.

Does doubling the distance really quarter the dose rate?

Exactly, for a point source in empty space, and the reason is geometry rather than physics: the same photons spread over the surface of a sphere, whose area goes as the square of the radius. It stops being exact in two places. CLOSE IN, inside about three times the source’s own longest dimension, the source is not a point and the law over-states the rate — which is the safe direction but makes contact-dose estimates useless. FAR OUT, air absorption and scatter start to count: a half-value layer of air at caesium-137 energies is about 75 metres, so a hundred-metre path transmits around 40 per cent of what the geometry alone predicts, and ground scatter adds some back. Between a few centimetres and a few tens of metres the inverse square law is the dominant term by a wide margin and the rest is a correction.

Why does this page refuse yttrium-90?

Because yttrium-90 is a pure beta emitter, and a gamma dose-rate formula applied to it would return a number near zero that a reader could take for “no external hazard”. Yttrium-90 is a serious external hazard. Its betas make bremsstrahlung in whatever stops them — a genuine penetrating dose, and one that gets WORSE in a high-Z shield, which is why a yttrium-90 vial is shielded with perspex first and lead second rather than with lead alone. And the betas themselves deliver a large skin dose at contact: a maximum energy of 2.28 MeV and a range of the order of a centimetre in soft tissue, which is metres in air, because a particle range is a mass per unit area and air is 880 times less dense than tissue. None of that is air kerma from a point source and none of it is visible to this calculation, so the page returns nothing rather than something misleading. Strontium-90 is refused for the same reason, with the additional point that its daughter yttrium-90 is in equilibrium with it and is also a pure beta emitter.

How do I convert an old R·cm²/(mCi·h) gamma constant?

Multiply by 23.68 to get µGy·m²/(GBq·h). The factor is three conversions in one: one roentgen is 8.76 mGy of air kerma (from the roentgen’s definition of 2.58×10⁻⁴ C/kg and a mean energy per ion pair in air of 33.97 J/C), one millicurie is 0.037 GBq, and a square centimetre is 10⁻⁴ of a square metre. So caesium-137’s 3.3 becomes 78.1, cobalt-60’s 13.2 becomes 312.5, iridium-192’s 4.8 becomes 113.6 and radium-226’s 8.25 becomes 195.3. Note that this conversion changes the units and not the quantity: both numbers are AIR KERMA. A constant published in mSv·m²/(GBq·h) of ambient dose equivalent is a different quantity, roughly 20 per cent larger at caesium energies, and is not interchangeable with either.

Is air kerma the same as dose, or as dose equivalent?

No, and the three get used interchangeably in a way that costs about a fifth. AIR KERMA is the kinetic energy released per unit mass of air and is what this page computes, in grays. ABSORBED DOSE to tissue is a different medium: the ratio of mass energy-absorption coefficients of ICRU-44 soft tissue to air, computed from the NIST tables this page already uses, is 1.051 at 30 keV, 1.095 at 100 keV and 1.102 from a few hundred keV upward, so tissue dose runs 5 to 10 per cent above air kerma. AMBIENT DOSE EQUIVALENT H*(10), which is what a survey meter is calibrated in and what a dose limit is written in, is larger again: the shielding pages on this site carry about 1.20 Sv/Gy at caesium-137’s 662 keV, taken at second hand from a published Health Physics Society answer which attributes it to a copyrighted ICRU report that neither they nor this page reproduce, and the ratio is energy-dependent. So treating a microgray of air kerma as a microsievert of H*(10) under-states by about 20 per cent at caesium energies, in the unsafe direction. This page stays in air kerma throughout and says so, rather than applying a conversion that depends on an energy spectrum it does not have.

Can I use this for an X-ray tube?

No, and not because of the arithmetic. An air kerma rate constant is a property of a radionuclide’s decay scheme: so many photons of such-and-such energies per decay. A tube has no decay scheme, no activity and no characteristic constant — its output depends on tube current, tube potential, filtration, target angle and target material, and it is MEASURED rather than computed, usually as an air kerma rate at a reference distance per unit of tube current. The inverse square part of this page applies perfectly well to a tube; the Γ·A part does not. For scattered radiation from a tube or from a patient, neither part applies: scatter is not a point source and does not follow a single inverse square law from any one place.

How thick a shield do I need to bring the rate down to a target?

This page will tell you what a thickness you propose actually does, and the shield-thickness page on this site does the inverse arithmetic — but neither answers the question as asked, and the reason is not modesty about the algebra. A required thickness depends on a dose constraint, an occupancy factor, a workload, a distance and a regulator, and it depends on BUILD-UP, which a narrow-beam calculation cannot see: published half-value layers are 11 to 33 per cent larger than ln2/μ because scattered photons arrive at the far side of a real shield from directions the beam never pointed in. So a narrow-beam answer under-states what a room needs, which is the unsafe direction. Use the numbers here to understand the problem and to check somebody else’s arithmetic; design with a build-up factor or a Monte Carlo calculation, and then survey it.

Why is the first-principles sum always a bit low?

Because it is a sum over PRINCIPAL GAMMA LINES and real decays emit more than those. Three things are missing. The many weak lines, each a fraction of a per cent, which together add a little. The characteristic X-rays that follow electron capture and internal conversion, which for a clean beta emitter are negligible and for an electron-capture nuclide can be most of the air kerma. And annihilation radiation where a positron branch exists. For cobalt-60, caesium-137, iridium-192 and iodine-131 the shortfall is 2 to 7 per cent and the derivation is a genuine check. For iodine-125 it is a factor of five and the derivation is not a check on anything. The one exception in the other direction is cobalt-57, where including a 14.41 keV line that the published constants cut off makes the sum 49 per cent too HIGH — so the rule is that a gamma-only sum is low ABOVE the cut-off, not low in general.

Related calculators

References

A. Pearce, NPL Report IR 6: Recommended Nuclear Decay Data, National Physical Laboratory. Crown copyright — cited, not reproduced, and used here through this plugin’s `_nuclide_data.py` for the gamma line energies and emission probabilities that the air kerma rate constant is derived from. VIA THE DATA MODULE. The lines matter more here than on the decay pages, because the derivation is a sum over them: caesium-137 contributes one line at 661.657 keV with a yield of 0.851, cobalt-60 two at 1173.228 and 1332.492 keV at essentially one each, and iridium-192 nine between 205.794 and 612.462 keV summing to 2.135 photons per decay. The list is of PRINCIPAL GAMMA lines only, which is the whole reason the derived constant is a few per cent below the published one for a clean gamma emitter and a factor of several below it for an electron-capture nuclide.
J. H. Hubbell and S. M. Seltzer, Tables of X-Ray Mass Attenuation Coefficients and Mass Energy-Absorption Coefficients, NIST Standard Reference Database 126, physics.nist.gov/PhysRefData/XrayMassCoef/. VIA THE DATA MODULE: the 369 rows these pages use were transcribed into this plugin’s `_nist_data.py` on 7 October 2026 and verified there — every absorption edge at its published energy, μ/ρ at 1 MeV matching the published spot value for all eight materials to the last printed digit, and μ_en/ρ at or below μ/ρ in every row — and the tables themselves were not re-fetched for this batch. A work of the United States Government and therefore free of domestic copyright, which is the reason this vertical can print the coefficients at all. TWO DIFFERENT COLUMNS of it matter here and are easy to confuse: μ/ρ is what is removed from a beam and is what attenuates a dose rate through a shield; μ_en/ρ is what is DEPOSITED and is what turns a photon fluence into an air kerma. The air kerma rate constant derivation on the dose-rate page uses the second; the shielding rows on the same page use the first.
CODATA recommended values of the fundamental physical constants as adopted in the 2019 SI, used through `_nuclide_data.py` for two exact numbers in the air kerma rate constant derivation: the Avogadro constant and the electronvolt, 1 keV = 1.602176634×10⁻¹⁶ J, which is now exact by definition. The third constant in the conversion is not CODATA’s and is worth naming because it is the one people get wrong: the roentgen is defined as 2.58×10⁻⁴ C/kg and the mean energy per ion pair in air W/e is 33.97 J/C, so one roentgen is 8.76 mGy of AIR KERMA. That is the factor that converts the old R·cm²/(mCi·h) gamma constants into µGy·m²/(GBq·h), and it is the independent route that confirms the derivation on the dose-rate page to within 2 to 7 per cent for four nuclides.
Avoidance of Serious X-Ray-Induced Skin Injuries to Patients During Fluoroscopically-Guided Procedures, Public Health Advisory, United States Food and Drug Administration, 9 September 1994 (read 7 October 2026). A US Government work and reproduced. Three things are taken from it. The dose rate: “The absorbed dose rate in the skin from the direct beam of a fluoroscopic x-ray system is typically between 0.02 and 0.05 Gy/min (2 and 5 rad/min), but may range from 0.01 to more than 0.5 Gy/min”, against a federal limit near 0.2 Gy/min for high-level control. The consequence it draws from that, which is the reason the page exists: “even typical dose rates can result in skin injury after less than one hour of fluoroscopy”. And three threshold doses from its Table II: early transient erythema at 2 Gy, moist desquamation at 15 Gy and dermal necrosis at 18 Gy, with times to onset of about 1.7 hours, four weeks and more than ten weeks respectively. The advisory is thirty-two years old and its equipment assumptions are dated; the thresholds and the arithmetic are not.
Backgrounder on Biological Effects of Radiation, United States Nuclear Regulatory Commission, nrc.gov (read 7 October 2026). A US Government work and reproduced. The source for the background comparison figure: “On average, a U.S. resident receives an annual radiation exposure from natural sources of about 310 millirem (3.1 millisieverts)”, with man-made sources adding roughly another 310 for a total of about 620 mrem a year, of which computed tomography alone is about 150. It also notes that radon and thoron account for two thirds of the natural component, which is the reason the figure varies so much between places and the reason the field is editable on this page: the average is a national average over a quantity dominated by local geology.